Did I answer this correctly?

1. Popcorn sales in movie theaters break down as 40% plain popcorn and 60% buttered popcorn. While 65% of the plain popcorn is purchased by adults, 80% of the buttered popcorn is purchased by children. If a child purchases popcorn, what is the probability that it is buttered popcorn?

When you figure up everything you get:
Plain popcorn bought by adults-.40*.65=.26 or 26%
Plain Popcorn bought by children-.40*(1-.65)=.40*.35=.14 or 14%
Buttered Popcorn bought by the children-.60*.80=.48 or 48%
Buttered Popcorn bought by adults-.60*(1-.80)=.60*.20=.12 or 12%

Since 48% of all popcorn is buttered popcorn bought by children and 14% of all plain popcorn is bought by children then when you add those two together to get the total amount of popcorn bought by children you get 62%.

Probability of a child buying popcorn is buying buttered popcorn=.48/.62=.77419 or 77.42%

1. Popcorn sales in movie theaters break down as 40% plain popcorn and 60% buttered popcorn. While 65% of the plain popcorn is purchased by adults, 80% of the buttered popcorn is purchased by children. If a child purchases popcorn, what is the probability that it is buttered popcorn?

When you figure up everything you get:
Plain popcorn bought by adults-.40*.65=.26 or 26%
Plain Popcorn bought by children-.40*(1-.65)=.40*.35=.14 or 14%
Buttered Popcorn bought by the children-.60*.80=.48 or 48%
Buttered Popcorn bought by adults-.60*(1-.80)=.60*.20=.12 or 12%

Since 48% of all popcorn is buttered popcorn bought by children and 14% of all plain popcorn is bought by children then when you add those two together to get the total amount of popcorn bought by children you get 62%.

Probability of a child buying popcorn is buying buttered popcorn=.48/.62=.77419 or 77.42%